Supplementary Information
Solvation Free Energies and Hydration Structure of N-methyl-p-nitroaniline
Alauddin Ahmed and Stanley I. Sandler †
Department of Chemical Engineering and Biomolecular Engineering, University of Delaware,
Newark, DE 19716
†Author to whom correspondence should be addressed (sandler@udel.edu)
This PDF file includes Force Field Parameters and Figures S1, S2(a), S2(b) and S3.
1
MNA Force Field [1]
Nonbonded Interactions:
12
𝜎𝑖𝑗
𝑈(𝑟𝑖𝑗 ) = 4𝜀𝑖𝑗 [( )
𝑟𝑖𝑗
6
𝜎𝑖𝑗
𝑞𝑖 𝑞𝑗
−( ) ]+
𝑟𝑖𝑗
4𝜋𝜀0 𝑟𝑖𝑗
where 𝑟𝑖𝑗 is the atom-atom separation distance; 𝜀𝑖𝑗 , 𝜎𝑖 are the Lennard-Jones well depth and
diameter, respectively; 𝑞𝑖 , 𝑞𝑗 are partial charge on 𝑖 and 𝑗 , respectively; 𝜀0 is permittivity of
vacuum.
Bond Stretching:
𝑈𝑏𝑜𝑛𝑑 =
𝑘𝑏
(𝑏 − 𝑏0 )
2
Where 𝑘𝑏 is the force constant, 𝑏 is the current bond length and 𝑏0 is the equilibrium bond
length.
Angle Bending:
𝑈𝑏𝑒𝑛𝑑 =
𝑘𝜃
(𝜃 − 𝜃0 )
2
Where 𝑘𝜃 is the force constant, 𝜃 is the current bond length and 𝜃0 is the equilibrium bond
length.
Torsion:
𝑛
𝑈𝑡𝑜𝑟𝑠 = ∑ 𝑐𝑖 (1 + 𝑐𝑜𝑠(𝑖𝜑 − 𝛿))
𝑖=1
Where 𝜑 is the dihedral angle, and 𝑐𝑖 are constants.
2
Table 1 Lennard-Jones Parameters for MNA (United Atom) [1]. Parentheses denote functional
group attached to the atom of interest.
𝜀(𝑘)
𝑞(𝑒)
𝜎(Å)
CH-(aro)
3.74
48
0
C-(NH)
4.50
15
0.187
N-(CH3)
3.52
58
-0.730
H-(N)
0.0
0.0
0.365
CH3
3.75
98
0.234
C-(NO2)
4.50
15
0.131
N-(O)
3.31
40
0.711
O-(N)
2.90
80
-0.449
Note: The partial charges were scaled by a factor of 0.94 in our calculations as used by
Sokkalingam et al. [1] in their octanol-water partition coefficient calculation.
Site
Table 2 Bond Stretching Parameters for MNA.
Bond
C-C
C-NO
O-N
C-NH
N-H
N-CH3
Bond length
(Å)
1.40
1.45
1.22
1.35
0.99
1.44
𝑘𝑏 ⁄2
(kcal/mol)
529.35
361.61
872.54
528.94
614.35
413.41
Table 3 Bending Parameters for MNA.
Bond
C-C-C
C-C-NO
O-N-C
O-N-O
C-C-NH
C-NH-C
H-N-CH3
Bond length
(degree)
120
120
111.50
125
120
112.9
112.9
3
𝑘𝜃 ⁄2
(kcal/mol)
189.40
154.80
167.90
181.10
145.40
73.90
72.90
Table 4 Torsional Parameters for MNA.
Bond
C-C-C-C
O-N-C-C
C-N-C-C
𝑛
𝛿
2
1,2
2,4
180
180, 180
180, 180
𝑐𝑖
(kcal/mol)
15.230
-0.136, 4.351
3.003, -0.308
0.12
0 .0
0 .0
0 .0
0 .0
Nu
20 9
1 8
1 7
1 6
1 5
1 4
1
m
be
ro
fs
13 2
1 1
1 0
1 9
ub
en
se
o
18
7
6
5
m
ble
s
4
3
2
ate
W
1
no
cta
l
0 .0
2
8
6
4
Probabilit
y of trans
itions
0.1
0
0
r
Figure S1 Probability distributions as a function of subensemble during the gradual insertion of
a single MNA molecule into water and 1-octanol solvents in the EE simulations.
4
0.5
a
PP+
Acceptance ratio
0.4
0.3
0.2
0.1
0.0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Number of subensembles
0.5
b
PP+
Acceptance ratio
0.4
0.3
0.2
0.1
0.0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Number of subensembles
Figure S2 Acceptance ratios of transitions between adjacent subensembles calculated during the
(a) hydration free energy calculation in water and (b) solvation free energy simulation in 1octanol using EE algorithm. The acceptance ratio of transitions from mth to (m-1)th subensemble
represented by 𝑃− and the acceptance ratio of transitions from mth to (m+1)th subensemble
represented by 𝑃+ .
5
25
20
15
m and Gm/kT
10
5
0
-5
-10
-15
-20
-25
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
m
Figure S3 The changes in free energy, 𝐺𝑚 ⁄𝑘𝑇 , and balancing factor,𝜂𝑚 , as a function of
insertion parameter (𝛼𝑚 ) where the subscript 𝑚, in all cases, represents the subensemble for
which the values are plotted and can be an integer value between 1 and 20. 𝜂𝑚 () in the
calculation of hydration free energy is compared with 𝐺𝑚 ⁄𝑘𝑇 (―) during the insertion of MNA
in water and 𝜂𝑚 () in the calculation of solvation free energy is compared with 𝐺𝑚 ⁄𝑘𝑇 (---)
during the insertion of MNA in 1-octanol.
6
References
1. N. Sokkalingam, M . H. Ketko and J. J. Potoff , “Physical property prediction of
energetic materials from molecular dynamics simulation”, a chapter in Energetic
Materials: Thermophysical properties, Predictions and Experimental Measurements
edited by V. Boddu and P. Redner (CRC Press, Boca Raton, 2010).
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